Nuclear magnetic resonance technology has been widely used to measure petrophysical properties of fluid containing porous media. Examples of such petrophysical properties include pore size, surface-to-volume ratio, formation permeability, and capillary pressure. In determining these properties, longitudinal relaxation time T1 and transverse relaxation time T2 are often of interest. Relaxation time is the time associated with nuclear spins to return to their equilibrium positions after excitation. The longitudinal relaxation time T1 relates to the alignment of spins with an external static magnetic field. Transverse relaxation time T2 is a time constant that identifies the loss of phase coherence that occurs among spins oriented to an angle to the main magnetic field. This loss is caused, in part, by the interactions between spins.
NMR log measurements can be performed using, for example, a centralized MRIL.RTM. tool made by NUMAR, a Halliburton company, or a sidewall CMR tool made by Schlumberger. The MRIL.RTM. tool is described, for example, in U.S. Pat. No. 4,710,713 to Taicher et al. Details of the structure and the use of the MRIL.RTM. tool, as well as the interpretation of various measurement parameters are also discussed in U.S. Pat. Nos. 4,717,876; 4,717,877; 4,717,878; 5,212,447; 5,280,243; 5,309,098; 5,412,320; 5,517,115, 5,557,200 and 5,696,448. A Schlumberger CMR tool is described, for example, in U.S. Pat. Nos. 5,055,787 and 5,055,788 to Kleinberg et al. U.S. Pat. No. 5,023,551 generally describes the use of NMR well logging. The content of the above patents is hereby expressly incorporated by reference.
The T2 distributions of brine-saturated rocks often reflect partial porosities of different pore sizes. The sum of the T2 amplitudes at different relaxation times, when properly calibrated, is equal to the total porosity. The amplitude of each relaxation time is equal to the partial porosity of that particular T2 relaxation time, and is related to a particular pore size.
When multiple pore fluids, such as oil, gas, and water, are present, it becomes somewhat difficult to differentiate them from their NMR signals especially when their T2 signals overlap. Methods have been proposed in the past to determine the type and quantity of the hydrocarbons contained in the pore space of rocks such as those described by Akkurt, R., Vinegar, H. J., Tutunjian, P. N., and Guillory, A. J., The Log Analyst, 37, 33 (1996). These methods use either different echo spacings, or different wait times, or combinations thereof, for Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences to obtain shifts or differences of T2 distributions for hydrocarbon identification and quantification, and sometimes for oil viscosity determination.
More elaborate methods, Chen, S., Georgi, D. T., Withjack, E. M., Minetto, C., Olima, O., and Gamin, H., Petrophysics, 41, 33 (2000) and Freedman, R., Sezginer, A., Flaum, M., Matteson, A., Lo, S., and Hirasaki, G. J., SPE Paper 63214, Society of Petroleum Engineers, Dallas, Tex. (2000), try to solve problems by analyzing the data analytically, or inverting data with different echo spacings and wait times simultaneously. But the successful applications of these methods heavily rely on the knowledge of the diffusion coefficients D of the unknown fluids. Whenever the T2 signals are insensitive to such manipulations, the result of such analysis becomes ambiguous and is sometimes inherently difficult such as when the T2 signal of the oil overlaps with that of irreducible water. The inversion algorithm is cast in a framework of a one-dimensional relaxation time distribution. The resulting data information is obtained and displayed in a one-dimension plot, i.e., the proton population as a function of T2 relaxation times. Further, information regarding internal field gradients within rocks cannot be readily extracted with regular CPMG pulse sequences to provide a full description of distributions of internal field gradients as a function of pore sizes.
Recently, it has been proposed by Hurlimann, M. D., Venkataramanan, L., Flaum, C., Speir, P., Karmonik, C., Freedman, R., and Heaton, N., “Diffusion Editing: New NMR Measurement of Saturation and Pore Geometry”, SPWLA Proc. 43rd Annual Logging Symposium, Oiso, Japan, Paper FFF (2002), that two-window type modified CPMG pulse sequences be used to acquire echo trains in magnetic field gradients thereby facilitating the acquisition of a 2D NMR proton distribution by the subsequent data inversion. Along with requiring special pulses sequences, the inversion algorithm requires two separable kernels to obtain the 2D NMR proton distribution. See U.S. patent applications 20020104326 and 20020067164, the contents of which are hereby incorporated by reference in their entirety. A related method has been reported by Sun, B. and Dunn, K-J., “Probing the internal field gradients in porous media”, Phys. Rev. E 65:051309 (2002). Unfortunately, these methods require significant modifications to current conventional logging tools to produce the desired two-window type modified CPMG pulse sequences. Also, the inversion algorithm requires the two kernels to be separable.